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Scientific Notation

Scientific notation is often used in physics to help express numbers that are extremely small or extremely large. It is important to have a good understanding of scientific notation.

 

To write a number in scientific notation:

1

Start with the original number

30,546.0

2,869,000.0

0.001 56

0.000 000 742 9

2

Write the first significant digit followed by a decimal point

3.

2.

1.

7.

3

Write the remainingsignificant figures on the right side of the decimal

3.0546

2.869

1.56

7.429

4

Count the number ofplaces you are shifting the decimal point*

4 to the left
or 4

6 to the left
or 6

3 to the right
or -3

7 to the right
or -7

5

Multiply by the appropriate power of 10. 

x 104

x 106

x 10-3

x 10-7

6

Number in Scientific Notation

3.0546 x 104

2.869 x 106

1.56 x 10-3

7.429 x 10-7

 

*Note – When the decimal is moved to the right, the power of 10 will be negative.  When the decimal is moved to the left, the power of 10 will be positive.